Abstract
In this paper, we prove some fixed point theorems for coupled-nonexpansive mapping and prove strong convergence and weakly convergence theorems for a double Mann-type iterative process to approximating a fixed point for coupled-nonexpansive operator in Hilbert spaces. Moreover, we prove some properties of the coupled fixed point set for coupled-nonexpansive mapping and prove fixed point theorem for such mapping on Banach spaces.
Highlights
Let (X, || · ||) be a real Banach space and let K be a nonempty subset of X
We prove some fixed point theorems for coupled-nonexpansive mapping and prove strong convergence and weakly convergence theorems for a double Mann-type iterative process to approximating a fixed point for coupled-nonexpansive operator in Hilbert spaces
We prove some properties of the coupled fixed point set for coupled-nonexpansive mapping and prove fixed point theorem for such mapping on Banach spaces
Summary
Let (X, || · ||) be a real Banach space and let K be a nonempty subset of X. In 2013, Olaoluwa et al.[8] introduced the definitions of nonexpansive condituon for coupled maps in product spaces and proved the existence of coupled fixed points of such mappings when X is a uniformly convex as follows: Definition 4. Berinde et al.[9] proved weak and strong convergence theorems for a double Krasnoselskijtype iterative method to approximate coupled solutions of a bivariate nonexpansive operator T : K × K → K, where K is a nonempty closed and convex subset of a Hilbert space as follows: Definition 6. We prove some fixed point theorems for coupled-nonexpansive mapping and prove strong convergence and weakly convergence theorems for a double Mann-type iterative process to approximating a fixed point for coupled-nonexpansive operator in Hilbert spaces. We prove some properties of the coupled fixed point set for coupled-nonexpansive mapping and prove fixed point theorem for such mapping on Banach spaces
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